where \(\odot \)  denotes the Hadamard (or entrywise) product. Problem
(REF ), or equivalently (REF ), is known as the
non-negative matrix scaling problem (see
e.g. [1]}, [2]}) and can be solved by an iterative method known as Sinkhorn's algorithm [3]},
\({\bf u}^{(i)} = {\bf f} \, \oslash \, (Q \, {\bf v}^{(i-1)}), \qquad {\bf v}^{(i)} = {\bf g} \, \oslash \, (Q^{\top } \, {\bf u}^{(i)}),\qquad i=1, \cdots , K.\) 
